Density of classical states in quantum theory@genneth: DFT is exact only theoretically. noone has ever found correct functional. it is like telling that using configurational integral is exact solution, but it is just rephrasing the problem.

How to find that a molecule has zero spin?Pauli exclusion priciple implies only that only 2 electrons can occupy 1 orbital. Energetic degeneracy of more distinct orbitals can cause some orbitals to be only singly occupied. There is also a Hund principle of maximum multiplicity (electrons having same spin repel less each other resulting in lower energy). So not all atoms/ions/compounds with even number of electrons have zero spin.